"Birthright citizenship" is a phrase loaded with good connotations. People tend to react well to the words "birth", "right", and "citizenship". (Consider their antonyms-"death", "wrong". and "treason".) The Boy Scouts award three merit badges with the word "citizenship" in the name. The Scouts emphasize the duties and obligations beholden in citizenship. That's what "citizenship" sounds like to the average patriotic American: doing right by your fellow Americans. They need to be reminded that, to the Zhous and Chaos of the world, it's just a sweet scam.

When you need a technical term for the current state of law, call it "jus soli". That's Latin for "law of ground". Nobody has a warm and fuzzy feeling about a couple of words they aren't sure how to pronounce. (It's pronounced y??s-so—le-.)

Similarly, let's use "anchor offspring" rather than "anchor babies". Babies are cute."

And as, as Steve goes on to point out, babies go on to grow up. Some one who was an adorable little baby in 1995 may be a full-fledged gang member today.